Farmer Bob, I'd recommend going to rvparkreviews.com to check for CGs outside the park on the east side. Most just outside the park are national forest CGs with small sites (not suited for large RVs) and no hookups, but there are some private ones between Cody & the east gate of Yellowstone. They may be listed under Cody but might be actually closer to YNP. That said, it's a good 1.5 - 2 hour drive from Cody to Yellowstone (one way).
I do advise checking on the fire situation in the park several times before you go. Right now, for example, there is a big backcountry fire that could cause some problems for the Fishing Bridge area.
Remember, Fishing Bridge is the only CG inside the park that has any hookups.
Good luck.